Paths to Triviality

Øgaard, Tore Fjetland

doi:10.1007/s10992-015-9374-6

Cited by 36 publications

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“…366f] showed that any such logic which also has the fusion connective will trivialize all of the mentioned naïve theories. 17 Fusion was therefore not adopted as a logical connective. One may, however, still try to work out a notion of suppression which restricts not only rules on the form B ∧ A → C B → C, but also B → (A → C) B → C. Finding a criterion for which such rules to deem suppressive, will then, just as in the extensional case, be the hard task.…”

Section: Speak Of the Devil And He Doth Appear: The Rhetorics Of Suppmentioning

confidence: 99%

Farewell to Suppression-Freedom

Øgaard

2020

Log. Univers.

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and onward that the variable sharing property is but a mere consequence of a good entailment relation, indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression of premises, therefore, gained center stage. Despite this, however, no serious attempt was ever made at analyzing the concept. This paper shows that their suggestions for how to understand it, either as the Anti-Suppression Principle or as the Joint Force Principle, turn out to yield properties strictly weaker than that of variable sharing. A suggestion for how to understand some of their use of the notion of suppression which clearly is not in line with these two mentioned principles is given, and their arguments to the effect that the Anderson and Belnap logics T, E and R are suppressive are shown to be both technically and philosophically wanting. Suppressionfreedom, it is argued, cannot do the job Plumwood and Sylvan intended it to do.

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Section: Speak Of the Devil And He Doth Appear: The Rhetorics Of Suppmentioning

confidence: 99%

Farewell to Suppression-Freedom

Øgaard

2020

Log. Univers.

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“…See[14, Sec. 9] for a triviality proof using ∀ = BB d strengthened by the rule version of E7.Australasian Journal of Logic (14:1) 2017, Article no.…”

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confidence: 99%

Skolem Functions in Non-Classical Logics

Øgaard¹

2017

AJL

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This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A(x,y) determines the extension of a function and f is a Skolem function for A.

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